MODELING AND OPTIMIZATION OF CRYOGENIC – OPTICAL ...

International Journal “Information Theories and Applications”, Vol. 19, Number 3, 2012

232

MODELING AND OPTIMIZATION OF CRYOGENIC – OPTICAL GRAVIMETERS

Vitaliy Yatsenko, Nikolay Nalyvaychuk

Abstract: This paper considers the problem of designing and developing optical-cryogenic devices using

optimization techniques, modeling, and new materials. We have shown how to produce reliable YBCO thin films

with controllable surfaces and physical properties and how to integrate them in a ring form into the optical-

cryogenic gravimeter so as to reduce its size and render it convenient for future space applications. Its function is

based on the magnetic levitation phenomenon of the probe and on the measurement of its displacement with

subsequent data processing.

Keywords: gravimeter, modeling, optimization, HTSC, YBCO, thin films, superconducting ring

ACM Classification Keywords: 1.6. Simulation and modeling, H.1 Models and principles. Optimization

Introduction

Since their discovery, the high temperature superconducting (HTSC) materials have always been a very

promising technology for integration in electronic multilayered assemblies, such as antennae, filters, SQUID-s etc.

due to their exotic properties.

YBa2Cu3O7-x (YBCO) has attracted a lot of research interest since it is still superconducting at temperatures

above that of liquid nitrogen (70 K) and exhibits the highest currents recorded in the literature, of the order of 108

A/cm2 [Vassiloyannis, 1999], enabling the construction of experimental devices highly sensitive in magnetic field

changes. In this paper we concentrate in an attempt to integrate YBCO thin films in a ring form into the gravimeter

described in [Yatsenko, 2003] in order to reduce its size and make it convenient for future space applications.

Highly monocrystalline good quality YBCO thin films can be reliably deposited onto SrTiO3 substrates by Pulsed

Laser Deposition (PLD) with Tc values ranging from 89 up to 91 K [Wellhofer, 1998]. Films grown on nominal

[001] substrates exhibit, however, non-controllable surface morphologies [Vassiloyannis, 1997], with island

growth and deep trenches in between which render the material unreliable for further integrations, since these

features tend to create undesired holes and joins between adjacent deposit layers. It has been shown [1] that

offcutting the STO substrate by 1.69o off the (001) towards the (100) plane allows the growth of smoother YBCO

films with a controllable surface morphology (with average surface roughness Ra ~ 1.05 nm, even less than the

YBCO unit-cell height) and with improved physical properties, i.e. an average current density Jc measured up to

108 A/cm 2 for B = 0.2 T and T = 4.2 K. In this report we propose the integration of 130-230 nm thick YBCO films

grown on 1.69o miscut STO substrates with single offcut direction [5] for the construction of a gravimeter.

The concept of the cryogenic-optical sensor

The sensor is based on a new type of free suspension of the probe of the superconducting gravimeter. Its

functioning is based on the magnetic levitation phenomenon of the probe and on the measurement of its

displacement with subsequent data processing. A free suspension of a probe can be realized using the

Braunbeck-Meisner phenomenon due to the ideal diamagnetism of a superconductor solid sphere. Our


233

conception is based on the zero electrical resistance of a closed coil, for example, a ring which, due to levitation,

may have a free equilibrium position. As a consequence of the superconducting phenomenon, the ring achieves

zero electrical resistance. At the same time, modern methods of signal processing are used for estimation of a

small perturbation (against a background of significant noise) which corresponds to parameters of the measured

gravitational field.

The newly developed superconducting gravimeter is represented by a spring type suspension. An analogue of

the mechanical spring of our device accomplishes the magnetic returning force acting on a superconducting

probe in a non-uniform magnetic field of superconducting rings or in a permanent magnet (in another variant).

Due to the high stability of the superconducting currents of the rings, a highly stable non-dissipative spring is

created.

The gravimeter is based on the following principle. In balance a probe is levitated in the position where the

gravitational force is compensated by the magnetic force which acts in the opposite direction. At a gravitation

change of the probe, it is moving from its zero position and an optical sensor measures an error signal. Due to

current change in a control ring, a self-tuning system creates an additional magnetic field that is proportional to

the signal which keeps the probe in zero position. Since the returning force is a linear function of the current, its

measurement in a control ring provides linear estimation of the gravitation force changes.

This suspension needs a high precision optical registration system for the probe displacement. It is proposed to

estimate the position of the probe by a laser sensor that allows to exclude the electric and magnetic fields which

affected the probe. For detection of supersmall displacements it is proposed to use a modern interferometry

method and dynamical effects of a laser signal constrained that correlates with mechanical displacement of the

probe. An interferometric method can provide a precision of coordinate measurement of the probe at most 0.1

nanomenter.

An experimental scheme with a laser displacement sensor has been selected and realized. This sensor provides

a conversion of a signal into the digital form for signal processing. Recently it has been shown that the optical

sensor based on a laser diode with an external resonator as a source of monochromatic radiation, and a single

mode optical fibers as a channel for light transportation to the probe preserving the coherence of an optical

radiation) satisfiy all the necessary requirements.

Several stages are used for signal processing in a cryogenic-optical gravimeter. The first stage consists of noise

compensation which influences the mechanical part of the device. The second stage is focused on the use of an

inverse dynamical model of the sensor. An adaptive digital filter is used at the third stage of signal processing. A

combination of a free probe suspension, the use of an optical registration system, and new tools of signal

processing provide new dynamic properties to our device.

Мodeling and Optimization

A fundamentally new optic-cryogenic sensor based on superconductive nanofilms has been grounded and

mathematically modeled. Also the problem of optimal supersmall acceleration estimation has been investigated.

The new principles of such sensor construction, has been proposed. We analyze the problem of the sensor

resistance using modern theoretical and experimental approaches. Also a model of a quantum device for optimal

information processing has been consodered. Solving of these problems requires further development of the

bilinear dynamical systems theory and investigation of chaotic regimes of the “10-10 g” dynamics. Taking into


234

account the sensor competitiveness and high sensitivity to gravitational perturbations, we plan to cover the device

by a patent. Also mathematical modeling of separate sensor components (superconductive suspension, laser

sensor and software) has been conducted. The modeling of the satellite sensor for micro-gravitational

perturbation estimations has been grounded. Moreover, nanomaterials suitable for constructing such

accelerometers have been determined. This will allow creation of adaptive micrometer-size gravimeter sensors

for microsatellites. In this chapter, we describe a superconducting gravity meter, its mathematical state. We have

also presented a mathematical model of the superconducting uspension which is based on a magnetic levitation.

A nonlinear control algorithm has been implemented for the purpose of maintaining chaotic behavior in the

sensor.

Nonlinear properties of a magnetic levitation system and an algorithm of a probe stability are studied. The

phenomenon, in which a macroscopic superconducting ring chaotically and magnetically levitates, is considered.

A nonlinear control scheme of a dynamic type is proposed for the control of a magnetic levitation system. The

proposed controller guarantees the asymptotic regulation of the system states to their desired values. We found

that if a non-linear feedback is used then the probe chaotically moves near an equilibrium state. An optimization

approach for selection of optimum parameters is discussed

The new recurrent RBF network architecture have been introduced as practical solutions to the noise cancellation

problem. It has been shown that the properties of the signals involved induce biased estimates of the filter

parameters in many practical cases. Although these effects can be eliminated by estimating a disturbance model,

it has been demonstrated that this additional

New filter realizations based on both the traditional and a new recurrent RBF network architecture have been

introduced as practical solutions to the noise cancellation problem. It has been shown that the properties of the

signals involved induce biased estimates of the filter parameters in many practical cases. Although these effects

can be eliminated by estimating a disturbance model, it has been demonstrated that this additional complexity

can be avoided by employing a new approach that mitigates the problem of bias without introducing excessive

computational complexity. Incorporating the ideas into a new RBF architecture provides an alternative structure to

traditional polynomial nonlinear filter design by combining the approximation capacity of the network with

unsupervised/supervised learning scheme comprising two separate consecutive stages, a k-means clustering

procedure and a suboptimal least-squares-based network updating strategy.

In contrast to the conventional recursive schemes, the latter can be implemented by performing a sequence of

Givens rotations in a highly efficient manner with numerical robustness. In addition, the inclusion of linear

dynamic link connections has been shown to enhance convergence. Finally, simulation examples have been

described to demonstrate the potential of the new RBF noise cancellation filter design. These results, coupled

with the on-line monitoring capabilities of the model validity tests, suggest that the new RBF filter provides an

appropriate structure for noise cancellation filter design. A comparison with earlier results given in Billings and EI-

Hitmy (1990), which employed various simpler linear and nonlinear polynomial models with the present design,

indicates that the new design framework based on the recurrent RBF network structure coupled with the hybrid

training algorithm exhibits excellent complexity can be avoided by employing a new approach that mitigates the

problem of bias without introducing excessive computational complexity.

Incorporating the ideas into a new RBF architecture provides an alternative structure to traditional polynomial

nonlinear filter design by combining the approximation capacity of the network with unsupervised/supervised

learning scheme comprising two separate consecutive stages, a k-means clustering procedure and a suboptimal


235

least-squares-based network updating strategy. In contrast to the conventional recursive schemes, the latter can

be implemented by performing a sequence of Givens rotations in a highly efficient manner with numerical

robustness. In addition, the inclusion of linear dynamic link connections has been shown to enhance

convergence. Finally, simulation examples have been described to demonstrate the potential of the new RBF

noise cancellation filter design. These results, coupled with the on-line monitoring capabilities of the model validity

tests, suggest that the new RBF filter provides an appropriate structure for noise cancellation filter design. A

comparison with earlier results given in Billings and EI-Hitmy (1990), which employed various simpler linear and

nonlinear polynomial models with the present design, indicates that the new design framework based on the

recurrent RBF network structure coupled with the hybrid training algorithm exhibits excellent.

Experiments

The superconducting gravimeter is a spring type gravimeter in which the mechanical spring is replaced by a

magnetic levitation of a superconducting sphere in the field of superconducting, persistent current coils. The

object is to utilize the perfect stability of supercurrents to create a perfectly stable spring. The magnetic levitation

is designed to provide independent adjustment of the total levitating force and the force gradient so that it can

support the full weight of the sphere and still yield a large displacement for a small change in gravity. The

gravimeters provide unequaled long term stability so that instrumental noise can be either below geophysical and

cultural noise or indistinguishable from it over periods ranging from years to minutes. This article reviews the

construction and operating characteristics of the instruments, and the range of research problems to which it has

been and can be applied. Support for operation of the instruments in the United States has been limited so that

operation of multiple instruments for periods much longer than a year has not been possible. However, some of

the most appropriate applications of the instrument will require records of several years from arrays of

instruments. Commercial versions of the instruments have now been purchased in sufficient numbers elsewhere

in the world so that a world-wide array has been organized to maintain instruments and share data over a period

of six years.

A YBa 2 Cu 3 O x7 thin film of 130-230 nm in thickness was grown onto a SrTiO 3 substrates vicinally offcut at

1.69o off the (001) towards the (100) plane. The substrate was firstly pre-annealed at 900oC for two (2) hours and

then studied using a Digital Instruments Nanoscope II AFM in air with the cantilever force at 8 nN in order to

evaluate its surface stepped structure. The YBCO film was subsequently deposited onto the substrate by Pulsed

Laser Ablation (PLD) with the specimen being heated during the whole process at a temperature of 820o C in an

oxygen atmosphere at a dynamical pressure of 0.4 Torr [3]. The film orientation with respect to the substrate c-

axis was examined by conventional θ-2θ scans using a Siemens D5000HR high resolution, four circle, six axis

diffractometer, with a CuKa source. Rocking curve experiments enabled measurement of the film full width at half

maximum (FWHM), whilst �-scans through the (018) YBCO peaks were conducted to evaluate the film in plane

alignment. The film surface was characterized using a Digital Instruments Nanoscope II STM (scanning tunneling

microscope) operating in constant current mode at a bias of 800 mV and a tunneling current of 50 pA. Average

magnetization measurements have been performed at temperatures of 4.2, 25, 50 and 77 K using an Oxford

Instruments Vibrating Sample Magnetometer (VSM).

The specimens firstly reached the required temperatures in zero field cooling mode and data were collected with

the field being increased up to 12 T at a sweep rate of 10 mTs 1 and then decreased down to 0 T. M-O images


236

were received of the specimen using a typical ferromagnetic iron garnet (Bix Lu3-xGayFe5-yO12) grown on a GGG

garnet (Gd3Ga3O12) ([1] and references therein) in combination with a mercury arc light source and filter. The

polarizer/analyzer system maintained stable at all processing times at an extinction angle of 6o off their crossed

position. A CCD camera with various shutter speeds (from 1/120 up to 1/40000 s-1 of a Nikon Optiphot 100S

optical microscope with a x5 objective lens and a 60 W white light was used to capture the M-O images.

Results

X-ray Characterisation: A sharp superconducting transition at ~ 90 K has verified the good superconducting

character of the specimen under study [Vassiloyannis, 1999]. A full width at half maximum (FWHM) value of

0.3212o for the (005)YBCO reflection confirmed the onocrystalline nature of the film. θ-2θ diffractograms with only

(001) peaks of the film and the substrate verified only one crystalline phase of the film with its c-axis aligned along

the substrate c-axis[Vassiloyannis, 1999]. The �-scan diagrams captured evidenced the absence of impurity

phases or of grains of different orientation on the film [Vassiloyannis, 1999].

AFM-STM Evaluation: The data received during the AFM study on the STO substrate after the preanneling

treatment revealed a uniformly shaped substrate surface. An image received of a representative area 1×1 m2 of

the substrate surface is shown in Fig. 1 as a “top view” plot with the color scale representing the height above the

lowest point of the AFM scan: steps uniformly shaped with a width of 114 nm and a height of 2.93 nm were visible

along the (100) direction demonstrating the sample offcut direction, while some rare steps smaller in width were

also seen along the (010) and (110) directions. The steps consist of several STO unit cells in height (STO unit cell

height ~ 0.389 nm ([Vassiloyannis, 1999], and references therein)), while they are also larger in width than the

STO unit cell as expected by the specimen offcut angle. The stepped structure of the substrate influenced the

structure of the film deposited, the surface structure of which also followed a well consistent stepped morphology.

In that case, as can be seen in the 0.5×0.5 µm2 image shown in Fig. 2., the YBCO film surface also consists of

almost single oriented steps, with an average surface roughness Ra=1.05 nm (even smaller that the YBCO unit

cell height, 1.12 nm [Vassiloyannis, 1999], , while some smaller steps are also distinguished along the (110)

direction.

Figure 1 – AFM-image of the 1.69° off cut STO substrate


237

Figure 2 – Corresponding STM-image of the YBCO film

grown

Figure 3 – Schematic representation of a

superconducting ring 0.5 mm in diameter (purple area)

on a 5.5 mm2 YBCO thin film platelet with outer radius

2.5 mm and inner radius 2mm

VSM Measurements: The magnetic hysteresis half-loops received by the VSM measurements are symmetrical

for fields above 0.2 T for all temperatures [Wellhofer, 1998]. Therefore, the average current density flowing within

the film can be extracted according to the Bean model and references therein) using the following formula:

Jc = 240(M/t) (1)

where M is in emu, t in cm and J с in A/cm 2 . The average current density dependence over field increase for

the four (4) different temperatures studied for the 1.69 0 sample are illustrated in figure 4. A top value of 6x10 11

Am 2 is captured for B=0.2 T and T=4.2 K.

Figure 4 – Average current density Jc for the 1.69° specimen extracted by VSM hysteresis loop measurements


238

Figure 5 – Top-view M-O image of the 1.69° film for full penetration

of the external field at T=25 K and B=103.8 mT

Figure 6 –Jc current densities in the parallel (blue) and perpendicular (pink) direction of the specimen [100]

direction. Jc current densities in the parallel (blue) and perpendicular (pink) direction of the specimen [100]

direction

M-O Analysis: A M-O image captured of the 1.69o sample at T=25 K and B=103.8 mT (full field penetration into

the sample) is illustrated in Fig.5. as top-view image, with the color gradient representing the field gradient within

the platelet [Vassiloyannis, 2006]. The color gradient corresponds to field numerical values and, thus, the current

density within the sample can be extracted inverting the Maxwell equation: B = 0 Ј (for E = 0). To achieve

the inversion a Pascal program is used [Vassiloyannis, 1997], based on the formula:


239

2

0 2/522

2

])(|[|

||)(2)(

4

1),( dd

d

dgdH

t

sZ

(2)

The grey profile of the image in Fig. 6 corresponds to the 3-D field distribution within the film. Two crossed lines

have therefore been selected, which passed from the specimen center, shown in Fig.6. top plot. After the

inversion process the corresponding crossed lines which passed from the current distribution profile center (the

“inverted” surface) were depicted and are illustrated in Fig. 6 bottom plot. The currents along the crossed lines

(“blue” [100] and “pink” [010] specimen directions) are equal, thus no discernible anisotropy is detected rendering

the 1.69o specimen reliable for the gravimeter rings.

HTSC Ring Construction: The YBCO film grown can be used for integration into the gravimeter proposed in

[Yatsenko, 2003]. The main measurement device is based in 2 rings of a conventional low temperature

superconductor (niobium-titanic) of a 2.38 cm inner diameter and 2.5 cm outer radius. The top plane of the probe

is polished in order to be used as a reflecting plane for the laser registration system. The gap for levitation,

depending on the weight of the probe, is selected from 7 mm up to 15 mm. Such working models have been

investigated theoretically and experimentally in the frame of the system suspension registration sensor. In

particular, the presence of an additional ferromagnetic mass on the probe has been analyzed. The influence of

the passive filter on the accuracy of the measurements has also been studied.

We propose the replacement of the conventional superconductor rings by rings patterned on HTSC platelets of

the type of the 1.69o specimen developed. The proposed HTSC ring is schematically illustrated in Fig. 6: the

surface of the film platelet is 5 ×5 mm2, while its thickness is ~200 nm (dark rectangular “marble area”). A HTSC

ring of 2.5 mm outer radius and 2 mm inner radius (“purple” area), with a thickness of ~ 200 nm can be patterned

by either optical (UV) or electron beam patterning. For the rings replacement it is also necessary to reduce the

dimensions of the gravimeter of [2] to 1/10 of the current device.

Conclusions

We describe a new gravimeter, which is suitable for long-term continuous observations. It uses laser

interferometry to measure the acceleration of a falling corner cube with reference to atomic standards. Between

drops, the corner cube is lifted to the top by rotating the vacuum pipe around a horizontal axis with an angular

velocity high enough to keep the cube fixed by centrifugal force. This method has an enormous advantage for

making a large number of measurements since there is no complicated mechanism inside the vacuum pipe. This

absolute gravimeter seems to have no source of systematic error which will exceed one part in 109 if we can

reduce the amplitude of the mechanical vibration to less than about 1.5 nm. We describe here the principle and

the results of the experiments that we have made to date.

In this paper, we have shown how to integrate YBCO thin film rings into the optical-cryogenic gravimeter in order

to reduce its size and make it convenient for future space applications. Its function is based on the magnetic

levitation phenomenon of the probe and on the measurement of its displacement with subsequent data

processing. A free suspension of the probe is realized using the magnetic potential well effect. Preliminary

experimental investigations have shown that the developed sensor can provide a displacement measurement


240

precision for the probe of ~ 0.1 nanometer, which corresponds to a measurement precision for the Earth's gravity

field acceleration at a level of ~ 10-10 g.

We report in this paper the results of a measurement of the gravitational constant G obtained in a laboratory at

distances of about 1 m, using a superconducting gravimeter. The instrument measured the gravitational effect

due to an annular mass of about 330 kg moving up and down around the gravimeter. The experiment yielded for

the gravitational constant the value G _=_(6:679 - 0:008) 10-11Nm2 /kg2 which agrees, within its uncertainty, with

the last CODATA valu anometer, which corresponds to a measurement precision for the Earth's gravity field

acceleration at a level of ~ 10-10 g.

Bibliography

[Vassiloyannis, 1999] D. Vassiloyannis. The Effect of Substrate Vicinal Offcut on the Morphology and Physical

Properties of YBa2Cu3O7-x Thin Films // IEEE Trans. on Appl. Superconductivity, 9(2) (1999) 1638-1643.

[Yatsenko, 2003]. V. Yatsenko, T. Bekmuratov, V. Kozorez, V. Kunzevich, Kh. Ismaili, O. Nabiyrv, O.Negriyko. O.

Cheremnichm, L. Yatsenko, S. Jivilo. Development of the cryogenicoptical sensor for high-sensitivity gravitational

measurements // Space Sciences and Technologies, 9(5/6) 71-78.

[Wellhofer, 1998] F. Wellhofer, P. Woodall, D. J. Norris, S. Johnson, D. Vassiloyannis et al. The Effect of

Substrate-Off-Cut on the Properties of Epitaxial Thin Films of YBa2Cu3O7-x Grown by Pulsed Laser Deposition //

Appl. Surf. Sci., 127-129 (1998) 525-532.

[Vassiloyannis, 1997] D. Vassiloyannis et al. The Effect of Vicinal Offcut on the Morphology and Defect

Microstructure of YBa2Cu3O7-x Thin Films on (001) SrTiO3 // Inst. Phys. Conf. Ser. 153,:Section 10, 1997.

[Vassiloyannis, 2006] D. Vassiloyannis. Magneto-optical Investigation on Miscut YBa2Cu3O7-x Thin Films on

SrTiO3 // Physica C, 3(2006).

Authors’ Information

Vitaliy Yatsenko – Head of Department of Remote Sensing Methods and Advanced Instrumentation, Space

Research Institut of NASU-NSAU,Ukraine,03680, Kyiv, Academika Glushkova str., 40; e-mail:

[email protected]

Nikolay Nalyvaychuk – Ggraduate Student,Department of Applied Mathematics, Kiev National Technical

University of Ukraine,(NTUU KPI), Ukraine, 03056, Kyiv, Prospect Peremogy 37; e-mail:

[email protected]

Area of research: remote sensing, space instrumentation

MODELING AND OPTIMIZATION OF CRYOGENIC – OPTICAL ...

Documents

Transcript of MODELING AND OPTIMIZATION OF CRYOGENIC – OPTICAL ...